Let \(X\)  be an symmetric, isotropic, log-concave vector in \(\mathbb {R}^m\) ; that is, it has a density that is a log-concave function (for an extensive survey on log-concavity and its role in Asymptotic Geometric Analysis, see [1]}, [2]}). Observe that \(X\)  satisfies the assumption of Theorem REF :
